Self-testing of multipartite GHZ states of arbitrary local dimension with arbitrary number of measurements per party

TL;DR

This paper introduces a novel self-testing scheme for multipartite GHZ states of any local dimension, requiring minimal measurements per party, advancing practical device-independent certification methods.

Contribution

It provides the first self-testing protocol for multipartite GHZ states of arbitrary local dimension without relying on qubit-specific results, using only two measurements per party.

Findings

Achieved self-testing of multipartite GHZ states of any local dimension.

Utilized a Bell inequality with maximal violation for certification.

Reduced the number of measurements needed for practical implementation.

Abstract

Device independent certification schemes have gained a lot of interest lately, not only for their applications in quantum information tasks but also their implications towards foundations of quantum theory. The strongest form of device independent certification, known as self-testing, often requires for a Bell inequality to be maximally violated by specific quantum states and measurements. In this work, using the techniques developed recently in [S. Sarkar et al., npj Quantum Inf. 7, 151 (2021)], we provide the first self-testing scheme for the multipartite Greenberger-Horne-Zeilinger (GHZ) states of arbitrary local dimension that does not rely on self-testing results for qubit states and that exploits the minimal number of two measurements per party. This makes our results interesting as far as practical implementation of device-independent certification methods is concerned. Our self-testing statement relies on maximal violation of a Bell inequality proposed recently in [R. Augusiak et al., New J. Phys. 21, 113001 (2019)].